Question

let u(x)=(u_1(x), u_2(x)) be a solution of the differential system u_1' = g_1(u_1,u_2), u_2' =g_2 (u_1,u_2)....

let u(x)=(u_1(x), u_2(x)) be a solution of the differential system u_1' = g_1(u_1,u_2), u_2' =g_2 (u_1,u_2). Show that if u(x_0 +w)=u(x_0) for some w>0, then u(x+w) =u(x) for all x>=x_0, i.e., u(x) is periodic of period w   

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The problem is to maximise utility u(x, y) =2*x +y s.t. x,y ≥ 0 and p*x...
The problem is to maximise utility u(x, y) =2*x +y s.t. x,y ≥ 0 and p*x + q*y ≤ w, where p=13.4 and q=3.9 and w=1. Here, * denotes multiplication, / division, + addition, - subtraction. The solution to this problem is denoted (x_0, y_0) =(x(p, q, w), y(p, q, w)). The solution is the global max. Find ∂u(x_0,y_0)/∂p evaluated at the parameters (p, q, w) =(13.4, 3.9, 1). Write the answer as a number in decimal notation with at...
Consider the differential equation:  . Let y = f(x) be the particular solution to the differential equation...
Consider the differential equation:  . Let y = f(x) be the particular solution to the differential equation with initial condition, f(0) = -1. Part (a) Find  . Show or explain your work, do not just give an answer.
Differential Geometry: Let a be a positive constant, and define x(u,v) := (v cos u, v...
Differential Geometry: Let a be a positive constant, and define x(u,v) := (v cos u, v sin u, a u), where 0 < u < 2π and v real. Compute the principal curvatures and the Gaussian curvature at each point of the surface defined by x.
Consider the differential equation y′′+ 9y′= 0.( a) Let u=y′=dy/dt. Rewrite the differential equation as a...
Consider the differential equation y′′+ 9y′= 0.( a) Let u=y′=dy/dt. Rewrite the differential equation as a first-order differential equation in terms of the variables u. Solve the first-order differential equation for u (using either separation of variables or an integrating factor) and integrate u to find y. (b) Write out the auxiliary equation for the differential equation and use the methods of Section 4.2/4.3 to find the general solution. (c) Find the solution to the initial value problem y′′+ 9y′=...
Let U(x,t) be the solution of the IBVP: Utt=4Uxx, x>0, t>0 ICs: U(x,0) = x, Ut(x,0)...
Let U(x,t) be the solution of the IBVP: Utt=4Uxx, x>0, t>0 ICs: U(x,0) = x, Ut(x,0) = 0, x>0 BCs: Ux(0,t) = 0 Find U(4,1) and U(1,2)
Solve the differential equation: x*(du(x)/dx)=[x-u(x)]^2+u(x) Hint: Let y=x-u(x) Answer: u(x)=x-x/(x-K) with K=constant
Solve the differential equation: x*(du(x)/dx)=[x-u(x)]^2+u(x) Hint: Let y=x-u(x) Answer: u(x)=x-x/(x-K) with K=constant
Find the solution to the system of differential equations: x' = y x(0) = 0 y'...
Find the solution to the system of differential equations: x' = y x(0) = 0 y' = 18x-3y y(0) = 1 Find: x(t) = ? y(t) = ?
Find the solution to the linear system of differential equations { x ′ = 17x−30y {...
Find the solution to the linear system of differential equations { x ′ = 17x−30y { y ′ = 10x−18y satisfying the initial conditions x(0)=−7 and y(0)=−5
Partial Differential Equation Problem: Find the general solution u(x, y) of: uxy = x2y. Show your...
Partial Differential Equation Problem: Find the general solution u(x, y) of: uxy = x2y. Show your work clearly.
let x=u+v. y=v find dS, the a vector, and ds^2 for the u,v coordinate system and...
let x=u+v. y=v find dS, the a vector, and ds^2 for the u,v coordinate system and show that it is not an orthogonal system
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT